Convergence analysis of chip- and fractionally spaced LMS adaptive multiuser CDMA detectors

This paper analyzes the convergence behavior of the least mean square (LMS) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited. The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of the transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, a initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the a noise subspace.

Gene-chip technology and its applications

Gene Chips are finding extensive use in animal and plant science. Generally microarrays are of two kind, cDNA or oligonucleotide. cDNA microarrays were developed at Stanford University, whereas oligonucleotide were developed by Affymetrix. The construction of cDNA or oligonucleotide on a glass slide helps to compare the gene expression level of treated and control samples by labeling mRNA with green (Cy3) and red (Cy5) dyes. The hybridized gene chip emit fluorescence whose intensity and colour can be measured. RNA labeling can be done directly or indirectly. Indirect method involves amino allyle modified dUTP instead of pre-labelled nucleotide. Hybridization of gene chip generally occurs in a minimum volume possible and to ensure the hetroduplex formation, a ten fold more DNA is spotted on slide than in the solutions. A confocal or semi confocal laser technologies coupled with CCD camera are used for image acquisition. For standardization, house keeping genes are used or cDNA are spotted in gene chip that are not present in treated or control samples. Moreover, statistical analysis (image analysis) and cluster analysis softwares have been developed by Stanford University. The gene-chip technology has many applications like expression analysis, gene expression signatures (molecular phenotypes) and promoter regulatory element co-expression.